In recent time several papers concerning signal separation of dynamically mixed source signals have been put forward [1-3, 8, 17, 19, 20]. In principle it is possible to separate the sources exploiting only second order statistics, cf. [8]. The blind signal separation problem with dynamic/convolutive mixtures is solved in the frequency domain in several papers presented, cf. [3, 20]. Basically, dynamic source separation in the frequency domain aims to solve a number of static/instantaneous source separation problems, one for each frequency bin in question. In order to obtain the dynamic channel system (mixing matrix), the estimates corresponding to different frequencies bins, have to be interpolated. This procedure seems to be a nontrivial task, due to scaling and permutation indeterminacies [16]. The approach in the present paper is a “time-domain approach”, see [8], which models the elements of the channel system with Finite Impulse Response (FIR) filters, thus avoiding this indeterminacies.
A quasi-maximum likelihood method for signal separation by second order statistics is presented by Pham and Garat in [11]. An algorithm is presented for static mixtures, i.e. mixing matrices without delays. Each separated signal si i=1, . . . , M is filtered with a Linear Time Invariant (LTI) filter hi. The criterion used is the estimated cross-correlations for these filtered signals. The optimal choice of the filter hi, according to [11], is the filter with frequency response inversely proportional to the spectral density of the corresponding source signal. The filters hi, i=1, . . . , M are thus whitening filters. However, the spectral densities of the source signals are usually unknown, and perhaps time varying. One approach is to estimate these filters as done in the present paper and in the prediction error method as presented in [1]. Moreover, several aspects of the algorithm presented in [8] remained open.